# Tagged Questions

Questions on the arbitrary precision capabilities of Mathematica.

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### When I can assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: machine-...
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### Meaning of backtick in floating-point literal

If I compute, say, 1/3//N, Mathematica displays 0.333333 as the result. When I copy that output to use elsewhere, the paste ...
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### Global precision setting

Coming from Maple I do not understand how the precision for numerical computations in Mathematica is specified. I understand that there are various options to commands such as ...
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### Arbitrary precision spline interpolation

The current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang says here that "it is not hard to implement it ...
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### Elegant high precision log1p?

Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
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### AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
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Is it possible to force Mathematica to perform computations with hardware supported quadruple-precision? The following test suggest, that all of the computations with fixed precision, different than <...
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### the winding number for the circle map (Arnold tongue)

I want to perform an iterative calculation and visualize the results: f[n_, a_, b_] := Nest[# + a - b Sin[2 π #] &, 0, n]/n; If I use machine precision, it ...
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I want to increase the precision globally to 50 at least, but $MinPrecision does not work. ... 1answer 388 views ### A problem with polynomial root finding I use the expression ... 1answer 695 views ### Preconditioning the objective function of NIntegrate for higher PrecisionGoal By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ... 1answer 361 views ### Accurately evaluating the hypergeometric function As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large$n$. I am hoping to obtain at ... 1answer 153 views ### Multidimensional arbitrary precision spline interpolation on the grid This question is a generalization of the previous one for multiple dimensions. In the answer to that question an implementation for the clamped spline interpolation for 1D case and arbitrary degree of ... 1answer 686 views ### Can some one explain perplexing behavior of arbitrary precision arithmetic? I was exploring the problem presented by another question, when I ran into some behavior of Mathematica's arbitrary precision arithmetic engine that perplexes me. Here is what I was doing ... 1answer 149 views ### A difficult precision problem I need to calculate values of a highly nonlinear recursive function, and I am confused by the results Mathematica is returning. ... 4answers 242 views ### Evaluating Erf[x] in arbitrary precision Is it possible to evaluate Erf[200] with arbitrary precision? I only get 1. as result but I would like to know if a arbitrary ... 2answers 135 views ### Why do I keep getting 0.06 with WorkingPrecision->1? I'm trying to generate a list of 1000 random numbers with WorkingPrecision->1. Is there any particular reason that I'm getting some entries as 0.06? I have tested the following lines: ... 1answer 127 views ### Machine-Precision and Arbitrary Precision [closed] What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision? 1answer 51 views ### Reals in Range; unexpected result for non-standard Precision I think I have encountered advice against using inexact numbers in specifications of ranges and iterator many times. I don't think I ever saw an example of unexpected results though, but today I found ... 1answer 328 views ### NDSolve with varying PrecisionGoal and WorkingPrecision Sometimes we need higher numerical precision to deal with large number cancellation in an equation. But if this cancellation happens only in a small (and known) parameter space, would it be possible ... 1answer 58 views ### MachinePrecision versus$MachinePrecision in NDSolve

I'd like to understand why one of these inputs gives me an error and the other doesn't: ...
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### How can I avoid these defects in ContourPlot3D output on WPC?

What I do: ContourPlot3D[-x^2/17.07 + y^2 + z^2 == 1 - x^17.07, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotPoints -> 16] What I get: ...
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### How to use adaptive precision in matrix computations?

I wish to compute the pseudo inverse of rectangular (or square) matrices by the cubically method of Chebyshev given by $X_{k+1}=X_k(3I-AX_k(3I-AX_k))$ where $X_0=\frac{1}{\|A\|_F^2}A^*$. The procedure ...
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### Manipulating an arbitrary-precision ContourPlot

I have a function, say minimizeme[ω_][β_][ϵ_] = ϵ^2 ω-Log[2 (Cosh[2 β]+Cosh[2 β ϵ])]/(2 β); I want to make a high-precision dynamic ...
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### Need more float precision

I have a Physics problem which huge and tiny numbers and Mathematica just gives me a speed of my particles which is the speed of light. Then $1/\sqrt{1-v^2/c^2}$ becomes singular. If I use smaller ...
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### Setting precision globally

This question is similar to this one and to this one. My code involves a lot of calls to Mathematica's N function, with the second argument (precision) set to 100 (say). I'm happy with the code, it ...
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### Physical quantities to decimal power

How can I get Mathematica to properly simplify physical quantities with dimensions to decimal power, such as $1 \frac{1}{\text{s}^{0.7}}\text{dynes}\text{/(}\text{cm}^2\text{Pa})$ that should simplify ...
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### How to tell Mathematica to treat all numbers (including those in decimal form) as arbitrary precision numbers

I have code that is essentially numerical. It uses functions like NDSolve and NIntegrate. But in most interesting cases, the ...
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### Set Global Maximum Precision

I'm sure this has been asked before, but I've looked around and can't figure it out: How do I set a global maximum precision for a notebook (or in general, globally)? I have a large notebook in ...
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### Making a calculation with high precision

I would like to make the following calculation: 1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1 Mathematica 8 returns 0. The result is obviously not 0, but my ...
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### Setting the Accuracy of calculations

I need to optimize an expression that involves a number of trigonometric functions and Exp[]. How do I make sure that all my calculations have an accuracy of 120-...
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### Is LinearSolve the most robust way to solve the equation $Ax=b$?

I want to solve the equation $Ax=b$, where $A$ is an $n\times n$ matrix, and $x$ and $b$ are $n\times 1$ column vectors. Here $n=124$. LinearSolve[A,b] I got the ...